Asymptotically optimal quantization and fusion in multiple sensor systems

The authors address the multiple sensor detection of a weak signal in dependent noise using quantizers and a fusion center. The model of dependence encompasses either m-dependent or ρ-mixing sequences. Two different sensor-function schemes are analyzed for dependence across time only and for dependence across both time and sensors. In the first case each sensor consists of a quantizer, and a test statistic is formed at the fusion center by summing the quantized data for each sensor. In the second case a nonlinear preprocessor is used to form a summed quantity before quantization at each sensor; it also assumed that a large number of quantization levels is used. In both cases, the summed quantities have Gaussian distribution under large sample size. The test statistics of both schemes have Gaussian distribution in the fusion center. The authors obtain the optimal quantizers and nonlinear preprocessors by maximizing the deflection induced from the Neyman-Pearson test of Gaussian data. They show that the complex optimization problem in the second case can be separated for each sensor into two decoupled optimization problems with respect to the quantizer on the one hand and the preprocessor on the other